Advanced Power Function in C++ [closed] - c++

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during my home task I had to create calculator that includes power function for rational numbers. At that time I wanted to create power function for complex and irrational numbers(something like modern calculator) using only pure c++. But unfortunately I could not find way even to represent complex and irrational numbers. So I'm stuck here.
Hope you can help me))

Answer 1

Edit: Apparently, you can use std::complex to try and solve your problem. Credit to #Pete Becker.
I'm just giving a suggestion here for complex numbers.
First, you can make a struct, where one member stores the constant of the real part, and one member stores the constant beside i in the imaginary part. You can store these as doubles.
i.e.
struct complex_num{
double real_part;
double complex_part;
}
Then, to compute a number raised to the complex number: we can do:
k^(a+bi) = k^a * k^bi
To calculate k^a, you can just use the built-in pow function.
To calculate k^bi, we need to use some more maths.
As you might know, k^bi can be written as (e^ln(k))^bi.
This can be rearranged to get (e^bi*ln(k))
e^((ln(k)*b)i) can be rewritten as cos(ln(k)*b) + i sin(ln(k)*b), which we can call q.
Hence: k^(a+bi) can be rewritten as pow(k,a) * q. This result can be stored in a variable of the type complex_num. I think to do the maths for this, all the functions you need are probably in the builtin maths library for c++.
I haven't got visual studio installed on my laptop so I can't check but I hope this helps.
If this hasn't outputted the right value, please reply to this so I can try and find the error and edit my answer.